A single-layer graphene metamaterial consisting of a horizontal graphene strip, four vertical graphene strips, and two graphene rings is proposed to realize tunable multi-plasma-induced transparency (MPIT) by the coupled mode theory and the finite-difference time-domain method. A switch with three modulation modes is realized by dynamically adjusting the Fermi level of graphene. Moreover, the effect of symmetry breaking on MPIT is investigated by controlling the geometric parameters of graphene metamaterials. Triple-PIT, dual-PIT, single-PIT can be transformed into each other. The proposed structure and results provide guidance for applications such as designing photoelectric switches and modulators.